1. Field
Various features relate to elliptic curve cryptography, particularly elliptic curve point multiplication procedures for use in generating digital signatures or the like.
2. Background
Elliptic curve (EC) point multiplication is a procedure used within EC cryptography that accepts a multiplier, k (sometimes called d), which is meant to be kept secret. EC point multiplication may be used, for example, as part of a procedure to create digital signatures for use in securing on-line transactions. Various techniques can be used by an attacker to obtain information pertaining to the secret multiplier k by exploiting side-channel leakage. For example, the amount of power consumed by a device performing EC point multiplication or the amount of time spent by the device performing the operations can potentially reveal information about k. In particular, problems can arise with conventional EC point multiplication procedures because certain operations involving zero consume less resources than those employing other values, resulting in possible leakage of information pertaining to k. One technique for addressing such leakage is to add a random multiple of n (where n is the order of the base point) to k. That is, k+(r*n) is employed rather than just k, where r is a random number. However, this technique does not ensure that operations involving zero will consume the same amount of time as operations on other values, and hence information leakage can still occur.
Therefore, there is a need to provide improved EC point multiplication procedures for use in generating digital signatures or for other purposes.